We present a modification of the DIRECT (DIviding RECTangles) algo- rithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem, since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema and un- available derivatives. DIRECT performs a sampling of the feasible domain over a set of points that becomes dense in the limit, thus ensuring the everywhere dense convergence; however, it becomes ineffective on significant instances of the problem under consideration, because it tends to produce a uniform coverage of the feasible domain, by oversampling regions that are far from the optimal solution. DIRECT has been modified by embodying information provided by a suitable discretization of the feasible domain, based on the signal theory, which takes into account the variabil- ity of the objective function. Numerical experiments show that DIRECT-G largely outperforms DIRECT and the grid search, the latter being the reference algorithm in the astrophysics community. Furthermore, DIRECT-G is comparable with a genetic algorithm specifically developed for the problem. However, DIRECT-G inherits the convergence properties of DIRECT, whereas the genetic algorithm has no guarantee of convergence.

Di Serafino, D., Liuzzi, G., Piccialli, V., Riccio, F., Toraldo, G. (2011). A modified DIviding RECTangles algorithm for a problem in astrophysics. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 151(1), 175-190 [10.1007/s10957-011-9856-9].

A modified DIviding RECTangles algorithm for a problem in astrophysics

PICCIALLI, VERONICA;
2011-01-01

Abstract

We present a modification of the DIRECT (DIviding RECTangles) algo- rithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem, since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema and un- available derivatives. DIRECT performs a sampling of the feasible domain over a set of points that becomes dense in the limit, thus ensuring the everywhere dense convergence; however, it becomes ineffective on significant instances of the problem under consideration, because it tends to produce a uniform coverage of the feasible domain, by oversampling regions that are far from the optimal solution. DIRECT has been modified by embodying information provided by a suitable discretization of the feasible domain, based on the signal theory, which takes into account the variabil- ity of the objective function. Numerical experiments show that DIRECT-G largely outperforms DIRECT and the grid search, the latter being the reference algorithm in the astrophysics community. Furthermore, DIRECT-G is comparable with a genetic algorithm specifically developed for the problem. However, DIRECT-G inherits the convergence properties of DIRECT, whereas the genetic algorithm has no guarantee of convergence.
2011
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/09 - RICERCA OPERATIVA
English
Con Impact Factor ISI
Global optimization; DIRECT algorithm; Detection of gravitational waves
http://link.springer.com/article/10.1007%2Fs10957-011-9856-9
Di Serafino, D., Liuzzi, G., Piccialli, V., Riccio, F., Toraldo, G. (2011). A modified DIviding RECTangles algorithm for a problem in astrophysics. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 151(1), 175-190 [10.1007/s10957-011-9856-9].
Di Serafino, D; Liuzzi, G; Piccialli, V; Riccio, F; Toraldo, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/70212
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